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|a (JST)25450021
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|a eng
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|a 15A52
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|a Bai, Z. D.
|e verfasserin
|4 aut
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| 245 |
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|a On Asymptotics of Eigenvectors of Large Sample Covariance Matrix
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|c 2007
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|a Text
|b txt
|2 rdacontent
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|a Computermedien
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|a Let $\{X_{ij}\}$, i, j =..., be a double array of i.i.d. complex random variables with EX₁₁ = 0, E|X₁₁|² = 1 and E|X₁₁|⁴ < ∞, and let $A_{n}=\frac{1}{N}T_{n}^{1/2}X_{n}X_{n}^{\ast }T_{n}^{1/2}$, where $T_{n}^{1/2}$ is the square root of a nonnegative definite matrix $T_{n}$ and $X_{n}$ is the n × N matrix of the upper-left corner of the double array. The matrix $A_{n}$ can be considered as a sample covariance matrix of an i.i.d. sample from a population with mean zero and covariance matrix $T_{n}$, or as a multivariate F matrix if $T_{n}$ is the inverse of another sample covariance matrix. To investigate the limiting behavior of the eigenvectors of $A_{n}$, a new form of empirical spectral distribution is defined with weights defined by eigenvectors and it is then shown that this has the same limiting spectral distribution as the empirical spectral distribution defined by equal weights. Moreover, if $\{X_{ij}\}$ and $T_{n}$ are either real or complex and some additional moment assumptions are made then linear spectral statistics defined by the eigenvectors of $A_{n}$ are proved to have Gaussian limits, which suggests that the eigenvector matrix of $A_{n}$ is nearly Haar distributed when $T_{n}$ is a multiple of the identity matrix, an easy consequence for a Wishart matrix.
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|a Copyright 2007 Institute of Mathematical Statistics
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|a Asymptotic distribution
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| 650 |
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|a Central limit theorems
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| 650 |
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|a CDMA
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|a Eigenvectors and eigenvalues
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| 650 |
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|a Empirical spectral distribution function
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| 650 |
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|a Haar distribution
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| 650 |
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|a MIMO
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| 650 |
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|a Random matrix theory
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| 650 |
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|a Sample covariance matrix
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|a SIR
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|a Stieltjes transform
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|a Strong convergence
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| 650 |
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|a Mathematics
|x Pure mathematics
|x Linear algebra
|x Matrix theory
|x Matrices
|x Covariance matrices
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| 650 |
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|a Mathematics
|x Pure mathematics
|x Linear algebra
|x Vector analysis
|x Mathematical vectors
|x Eigenvectors
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| 650 |
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|a Mathematics
|x Pure mathematics
|x Linear algebra
|x Matrix theory
|x Eigenvalues
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| 650 |
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4 |
|a Mathematics
|x Pure mathematics
|x Linear algebra
|x Matrix theory
|x Spectral theory
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| 650 |
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4 |
|a Mathematics
|x Pure mathematics
|x Probability theory
|x Random variables
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| 650 |
|
4 |
|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Descriptive statistics
|x Statistical sampling
|x Sampling methods
|x Random sampling
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| 650 |
|
4 |
|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Descriptive statistics
|x Statistical distributions
|x Distribution functions
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| 650 |
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4 |
|a Information science
|x Information search and retrieval
|x Information search
|x Search strategies
|x Truncation
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| 650 |
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4 |
|a Mathematics
|x Pure mathematics
|x Probability theory
|x Probabilities
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| 650 |
|
4 |
|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Descriptive statistics
|x Statistical distributions
|x Normal distribution curve
|x Sampling distributions
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| 650 |
|
4 |
|a Mathematics
|x Pure mathematics
|x Linear algebra
|x Matrix theory
|x Matrices
|x Covariance matrices
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| 650 |
|
4 |
|a Mathematics
|x Pure mathematics
|x Linear algebra
|x Vector analysis
|x Mathematical vectors
|x Eigenvectors
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| 650 |
|
4 |
|a Mathematics
|x Pure mathematics
|x Linear algebra
|x Matrix theory
|x Eigenvalues
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| 650 |
|
4 |
|a Mathematics
|x Pure mathematics
|x Linear algebra
|x Matrix theory
|x Spectral theory
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| 650 |
|
4 |
|a Mathematics
|x Pure mathematics
|x Probability theory
|x Random variables
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| 650 |
|
4 |
|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Descriptive statistics
|x Statistical sampling
|x Sampling methods
|x Random sampling
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| 650 |
|
4 |
|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Descriptive statistics
|x Statistical distributions
|x Distribution functions
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| 650 |
|
4 |
|a Information science
|x Information search and retrieval
|x Information search
|x Search strategies
|x Truncation
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| 650 |
|
4 |
|a Mathematics
|x Pure mathematics
|x Probability theory
|x Probabilities
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| 650 |
|
4 |
|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Descriptive statistics
|x Statistical distributions
|x Normal distribution curve
|x Sampling distributions
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| 655 |
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|a research-article
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1 |
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|a Miao, B. Q.
|e verfasserin
|4 aut
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|a Pan, G. M.
|e verfasserin
|4 aut
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|i Enthalten in
|t The Annals of Probability
|d Institute of Mathematical Statistics
|g 35(2007), 4, Seite 1532-1572
|w (DE-627)270938249
|w (DE-600)1478769-6
|x 00911798
|7 nnns
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|g volume:35
|g year:2007
|g number:4
|g pages:1532-1572
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|u https://www.jstor.org/stable/25450021
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|d 35
|j 2007
|e 4
|h 1532-1572
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